Drawing mountains: shadows

08 Jul 2026

After a couple of weeks of hiatus (sometimes, actual work needs to get done), we are back to our pointless but fun weekend project: drawing mountains in a style similar to topographic maps, using shadows to hint at the relief. We are pretty certain that this must be a solved problem. We aren’t particularly interested in the result: this is more of an excuse to understand lights, and do a bit of geometry.

As a recap and a teaser, we left off with a simple illumination model, where the tiles that represent our terrain were lighter or darker, depending on how much direct light they received:

This isn’t too bad, but it misses an important element: the shadow cast by the mountains. After our latest changes, this is how things look - much more satisfying:

Computing cast shadow

Let’s get this out of the way from the get-go: we got this working, but it is not pretty, and we might revisit this later on. With that said, let’s get into it.

Conceptually, the problem is not very complicated. Take a point on the surface of our terrain, and draw a line from that point, following the direction of the light downwards. If that line hits another point on the surface, that point is in the shadow of the first point, which blocks the light it would otherwise receive.

Practically, things are a little messy. The question we need to answer is not “is this point in the shadow of another point”, but “is this tile in the shadow of other terrain elements”. This is messy because there is no reason a tile should be entirely obscured or devoid of shadow. A tile is a surface, and each of its point could be obscured or not, causing the tile to be only partially obscured.

Rather than being correct, we chose to try the simplest thing that we could get to work, committing sins and making approximations along the way, so we could see how that worked out.

The general approach we followed was to assume that a tile was either in the shadow or not (as opposed to partially obscured). We determine that by starting from the mid-point of the tile, treating that point as if it were the tile. We “walk backwards” from that point, following the direction of the light, until we reach one of two cases:

• we find a location that would block the light (in what case the tile is “in the shadow”), or
• we are in the clear: we exited the map without encountering any light obstruction (no shadow).

How do we determine whether we found a location that would block the light? We used a dreadful approximation. When we follow the light backwards, we take discrete steps, and go through a series of coordinates (x, y, z). In other words, at position (x, y), the light that would hit our target tile is at altitude z. If the terrain altitude at that same position (x, y) is higher the light is blocked.

Unfortunately, we do not have that altitude readily available. What we have is the altitude at the 4 edges of each tile. Fortunately, we are not trying to be precise here, so we approximate the altitude of that location by taking the average of the altitudes of the 4 corners of the tile that contains it.

The relevant code is in the CastShadow module, and in the altitude function.

And that’s pretty much it. After we determined the amount of light a tile receives, we simply compute if its light is obstructed, and if so, we give it a darker shade.

Parting thoughts

Given how inelegant the whole approach was, we were pleasantly surprised that the result… kind of worked?

Before

After

Our initial idea was to go the other way around, and iterate over the known altitudes of the terrain (the edges of our tiles), following the light downwards until we hit a tile. Inverting the direction and going backwards, asking “is the light for this tile obstructed” ended up being more straightforward, but feels inefficient. One easy improvement would be to not follow the light until we exit the map, but stop when the altitude is higher than the highest altitude on the map.

That being said, the real question is, what should we do if we were not using our dirty approximation. The answer here is, we don’t know. From a geometry standpoint, it sounds like we would need to take each tile, project its cast shadow on a surface that is not that simple, the terrain, and possibly determine how much of each tile is shaded, to determine how dark it should be.

This does not sounds like an easy problem, so we gave up, at least temporarily. We have a nagging suspicion that we are not thinking about this right, and that perhaps there is a better way to represent the domain that simplifies some of these issues. Anyways, we will give it a rest for now, and maybe revisit it later!

In the meantime, you can check out the work in progress on Codeberg.